Question

How do you write $y + 5 = - 6(x + 7)$ in slope intercept form?

Answer 1

Hint: First we know that the slope-intercept form. Proportional linear functions can be written form $y = mx + b$, where $m$ is the slope of the line. Non-proportional linear functions can be written in the form $y = mx + b$,$b \ne 0$
We find $m$.
We just use the substitute, addition and division.
Finally we get the slope in the given linear equation.

Complete step-by-step solution:
The given equation is $y + 5 = - 6(x + 7)$
Slope intercept is written in the form of: $y = mx + b$
$m$ is the gradient of the line.
$b$ is the $y$ intercept
You can convert the given equation to the slope intercept form by simplifying the equation and group the like terms. Steps are as follow:
$ \Rightarrow y + 5 = - 6(x + 7)$
Expand the bracket by multiply$ - 6$with the inner components of the bracket.
$ \Rightarrow y + 5 = - 6x - 42$
Subtract both sides by $5$ to get $y$ on it’s on.
$ \Rightarrow y + 5 - 5 = - 6x - 42 - 5$
In LHS (Left Hand Side) subtract$5$by$5$ and RHS (Right Hand Side) add$42$by$5$, hence we get
$ \Rightarrow y + 0 = - 6x - 47$
The zero terms vanish
$ \Rightarrow y = - 6x - 47$

The equation in slope-intercept form is $y = - 6x - 47$.

Note: The slope-intercept form is probably the most frequently used way to express the equation of a line. Proportional linear functions can be written form $y = mx + b$, where $m$ is the slope of the line. Non-proportional linear functions can be written in the form $y = mx + b$,$b \ne 0$. This is called the slope-intercept form of a straight line because $m$ is the slope $b$ is the $y$-intercept.
The conditions are:
When $b = 0$ and $m \ne 0$, the line passes through the origin and its equation is $y = mx$.
When $b = 0$ and $m = 0$, the coincides with the $x$-axis and its equation is $y = 0$
When $b \ne 0$ and $m = 0$, the line is parallel to the $x$-axis and its equation is $y = b$.